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Homework Help: Optimization Problem - Calculus

  1. Mar 4, 2010 #1
    1. The problem statement, all variables and given/known data

    A cylindrical shaped tin can must have a volume of 1000cm3.

    Find the dimensions that require the minimum amount of tin for the can (Assume no waste material). The smallest can has a diameter of 6cm and a height of 4 cm.

    2. Relevant equations

    [tex]V = \pi r^{2}h[/tex]

    [tex]P = 2( \pi r^{2}) + (2 \pi r)h[/tex]

    3. The attempt at a solution

    I basically start off by isolating a variable:

    [tex]V = \pi r^{2}h[/tex]

    [tex]1000 = \pi r^{2}h[/tex]

    [tex]318.3 = r^{2}h[/tex]

    [tex]r^{2} = \frac{318.3}{h}[/tex]
    This is where I'm stuck. Do I plug this into the surface area formula.
    I know I have to sub this into something else, and then expand and find the derivative of that new equation to find where h > 4.
    Just need to find out what to do next from here.

    Thanks for any help!
  2. jcsd
  3. Mar 4, 2010 #2


    Staff: Mentor

    You have a relationship between r and h (but leave pi in - 1000/pi is not exactly equal to 318.8). Now rewrite your surface area function P (why is it P?) so that it is a function of one variable, either r or h. Then use the normal technique for finding the minimum or maximum function value.
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